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Constructing the disk method formula for the volume obtained by revolving a curve around an axis with the help of CAS
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2007-12-01
https://doi.org/10.5485/TMCS.2007.0167
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Copyright (c) 2007 Muharrem Aktümen and Tolga Kabaca
This work is licensed under a Creative Commons Attribution 4.0 International License.
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Aktümen, M., & Kabaca, T. (2007). Constructing the disk method formula for the volume obtained by revolving a curve around an axis with the help of CAS. Teaching Mathematics and Computer Science, 5(2), 363-376. https://doi.org/10.5485/TMCS.2007.0167
Abstract
Calculus concepts should have been taught in a carefully designed learning environment, because these concepts constitute a very important base for almost all applied sciences. The integral, one of the fundamental concepts of Calculus, has a wide application area. This paper focuses on constructing the disk method formula for the volume obtained by revolving a curve around an axis with the help of a CAS.
In this study, a semi-structured interview was carried out. In this interview, we tried to construct the disk method formula.
The levels of constructing the disk method formula in this study are:
• Introducing the concept: evaluating the volume of an Egyptian pyramid.
• Evaluating the volume of a cone obtained by revolution (using Maple worksheet).
• Designing their own ring and evaluating its price (using Maplet).
In this study, the interview has been presented as a dialog between teacher and students. When we look at feedback from students, we see that such a teaching method effects students in a positive way and causes them to gain conceptual understanding directed towards the concepts of approximation and volume.
In this study, a semi-structured interview was carried out. In this interview, we tried to construct the disk method formula.
The levels of constructing the disk method formula in this study are:
• Introducing the concept: evaluating the volume of an Egyptian pyramid.
• Evaluating the volume of a cone obtained by revolution (using Maple worksheet).
• Designing their own ring and evaluating its price (using Maplet).
In this study, the interview has been presented as a dialog between teacher and students. When we look at feedback from students, we see that such a teaching method effects students in a positive way and causes them to gain conceptual understanding directed towards the concepts of approximation and volume.